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org.apache.commons.math3.linear</FONT>
<BR>
Class SymmLQ</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.IterativeLinearSolver</A>
      <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver</A>
          <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.linear.SymmLQ</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>SymmLQ</B><DT>extends <A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></DL>
</PRE>

<P>
<p>
 Implementation of the SYMMLQ iterative linear solver proposed by <a
 href="#PAIG1975">Paige and Saunders (1975)</a>. This implementation is
 largely based on the FORTRAN code by Pr. Michael A. Saunders, available <a
 href="http://www.stanford.edu/group/SOL/software/symmlq/f77/">here</a>.
 </p>
 <p>
 SYMMLQ is designed to solve the system of linear equations A &middot; x = b
 where A is an n &times; n self-adjoint linear operator (defined as a
 <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear"><CODE>RealLinearOperator</CODE></A>), and b is a given vector. The operator A is not
 required to be positive definite. If A is known to be definite, the method of
 conjugate gradients might be preferred, since it will require about the same
 number of iterations as SYMMLQ but slightly less work per iteration.
 </p>
 <p>
 SYMMLQ is designed to solve the system (A - shift &middot; I) &middot; x = b,
 where shift is a specified scalar value. If shift and b are suitably chosen,
 the computed vector x may approximate an (unnormalized) eigenvector of A, as
 in the methods of inverse iteration and/or Rayleigh-quotient iteration.
 Again, the linear operator (A - shift &middot; I) need not be positive
 definite (but <em>must</em> be self-adjoint). The work per iteration is very
 slightly less if shift = 0.
 </p>
 <h3>Preconditioning</h3>
 <p>
 Preconditioning may reduce the number of iterations required. The solver may
 be provided with a positive definite preconditioner
 M = P<sup>T</sup> &middot; P
 that is known to approximate
 (A - shift &middot; I)<sup>-1</sup> in some sense, where matrix-vector
 products of the form M &middot; y = x can be computed efficiently. Then
 SYMMLQ will implicitly solve the system of equations
 P &middot; (A - shift &middot; I) &middot; P<sup>T</sup> &middot;
 x<sub>hat</sub> = P &middot; b, i.e.
 A<sub>hat</sub> &middot; x<sub>hat</sub> = b<sub>hat</sub>,
 where
 A<sub>hat</sub> = P &middot; (A - shift &middot; I) &middot; P<sup>T</sup>,
 b<sub>hat</sub> = P &middot; b,
 and return the solution
 x = P<sup>T</sup> &middot; x<sub>hat</sub>.
 The associated residual is
 r<sub>hat</sub> = b<sub>hat</sub> - A<sub>hat</sub> &middot; x<sub>hat</sub>
                 = P &middot; [b - (A - shift &middot; I) &middot; x]
                 = P &middot; r.
 </p>
 <p>
 In the case of preconditioning, the <A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolverEvent.html" title="class in org.apache.commons.math3.linear"><CODE>IterativeLinearSolverEvent</CODE></A>s that
 this solver fires are such that
 <A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolverEvent.html#getNormOfResidual()"><CODE>IterativeLinearSolverEvent.getNormOfResidual()</CODE></A> returns the norm of
 the <em>preconditioned</em>, updated residual, ||P &middot; r||, not the norm
 of the <em>true</em> residual ||r||.
 </p>
 <h3><a id="stopcrit">Default stopping criterion</a></h3>
 <p>
 A default stopping criterion is implemented. The iterations stop when || rhat
 || &le; &delta; || Ahat || || xhat ||, where xhat is the current estimate of
 the solution of the transformed system, rhat the current estimate of the
 corresponding residual, and &delta; a user-specified tolerance.
 </p>
 <h3>Iteration count</h3>
 <p>
 In the present context, an iteration should be understood as one evaluation
 of the matrix-vector product A &middot; x. The initialization phase therefore
 counts as one iteration. If the user requires checks on the symmetry of A,
 this entails one further matrix-vector product in the initial phase. This
 further product is <em>not</em> accounted for in the iteration count. In
 other words, the number of iterations required to reach convergence will be
 identical, whether checks have been required or not.
 </p>
 <p>
 The present definition of the iteration count differs from that adopted in
 the original FOTRAN code, where the initialization phase was <em>not</em>
 taken into account.
 </p>
 <h3><a id="initguess">Initial guess of the solution</a></h3>
 <p>
 The <code>x</code> parameter in
 <ul>
 <li><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><CODE>solve(RealLinearOperator, RealVector, RealVector)</CODE></A>,</li>
 <li><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><CODE>solve(RealLinearOperator, RealLinearOperator, RealVector, RealVector)</CODE></A>},</li>
 <li><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><CODE>solveInPlace(RealLinearOperator, RealVector, RealVector)</CODE></A>,</li>
 <li><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><CODE>solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector)</CODE></A>,</li>
 <li><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)"><CODE>solveInPlace(RealLinearOperator, RealLinearOperator, RealVector, RealVector, boolean, double)</CODE></A>,</li>
 </ul>
 should not be considered as an initial guess, as it is set to zero in the
 initial phase. If x<sub>0</sub> is known to be a good approximation to x, one
 should compute r<sub>0</sub> = b - A &middot; x, solve A &middot; dx = r0,
 and set x = x<sub>0</sub> + dx.
 </p>
 <h3><a id="context">Exception context</a></h3>
 <p>
 Besides standard <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception"><CODE>DimensionMismatchException</CODE></A>, this class might throw
 <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear"><CODE>NonSelfAdjointOperatorException</CODE></A> if the linear operator or the
 preconditioner are not symmetric. In this case, the <A HREF="../../../../../org/apache/commons/math3/exception/util/ExceptionContext.html" title="class in org.apache.commons.math3.exception.util"><CODE>ExceptionContext</CODE></A>
 provides more information
 <ul>
 <li>key <code>"operator"</code> points to the offending linear operator, say L,</li>
 <li>key <code>"vector1"</code> points to the first offending vector, say x,
 <li>key <code>"vector2"</code> points to the second offending vector, say y, such
 that x<sup>T</sup> &middot; L &middot; y &ne; y<sup>T</sup> &middot; L
 &middot; x (within a certain accuracy).</li>
 </ul>
 </p>
 <p>
 <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear"><CODE>NonPositiveDefiniteOperatorException</CODE></A> might also be thrown in case the
 preconditioner is not positive definite. The relevant keys to the
 <A HREF="../../../../../org/apache/commons/math3/exception/util/ExceptionContext.html" title="class in org.apache.commons.math3.exception.util"><CODE>ExceptionContext</CODE></A> are
 <ul>
 <li>key <code>"operator"</code>, which points to the offending linear operator,
 say L,</li>
 <li>key <code>"vector"</code>, which points to the offending vector, say x, such
 that x<sup>T</sup> &middot; L &middot; x < 0.</li>
 </ul>
 </p>
 <h3>References</h3>
 <dl>
 <dt><a id="PAIG1975">Paige and Saunders (1975)</a></dt>
 <dd>C. C. Paige and M. A. Saunders, <a
 href="http://www.stanford.edu/group/SOL/software/symmlq/PS75.pdf"><em>
 Solution of Sparse Indefinite Systems of Linear Equations</em></a>, SIAM
 Journal on Numerical Analysis 12(4): 617-629, 1975</dd>
 </dl>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>3.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: SymmLQ.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
<HR>

<P>

<!-- ======== CONSTRUCTOR SUMMARY ======== -->

<A NAME="constructor_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Constructor Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#SymmLQ(int, double, boolean)">SymmLQ</A></B>(int&nbsp;maxIterations,
       double&nbsp;delta,
       boolean&nbsp;check)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#SymmLQ(org.apache.commons.math3.util.IterationManager, double, boolean)">SymmLQ</A></B>(<A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</A>&nbsp;manager,
       double&nbsp;delta,
       boolean&nbsp;check)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a> and custom iteration manager.</TD>
</TR>
</TABLE>
&nbsp;
<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()">getCheck</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns <code>true</code> if symmetry of the matrix, and symmetry as well as
 positive definiteness of the preconditioner should be checked.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
      boolean&nbsp;goodb,
      double&nbsp;shift)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system (A - shift
 &middot; I) &middot; x = b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
      boolean&nbsp;goodb,
      double&nbsp;shift)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the solution to the system (A - shift &middot; I) &middot; x = b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
      <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solveInPlace</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)">solveInPlace</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x,
             boolean&nbsp;goodb,
             double&nbsp;shift)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system (A - shift
 &middot; I) &middot; x = b.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solveInPlace</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
             <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an estimate of the solution to the linear system A &middot; x =
 b.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.linear.<A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">checkParameters</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_org.apache.commons.math3.linear.IterativeLinearSolver"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class org.apache.commons.math3.linear.<A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">IterativeLinearSolver</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">checkParameters</A>, <A HREF="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#getIterationManager()">getIterationManager</A></CODE></TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ========= CONSTRUCTOR DETAIL ======== -->

<A NAME="constructor_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Constructor Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="SymmLQ(int, double, boolean)"><!-- --></A><H3>
SymmLQ</H3>
<PRE>
public <B>SymmLQ</B>(int&nbsp;maxIterations,
              double&nbsp;delta,
              boolean&nbsp;check)</PRE>
<DL>
<DD>Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a>. Note that setting <code>check</code> to <code>true</code>
 entails an extra matrix-vector product in the initial phase.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>maxIterations</CODE> - the maximum number of iterations<DD><CODE>delta</CODE> - the &delta; parameter for the default stopping criterion<DD><CODE>check</CODE> - <code>true</code> if self-adjointedness of both matrix and
 preconditioner should be checked</DL>
</DL>
<HR>

<A NAME="SymmLQ(org.apache.commons.math3.util.IterationManager, double, boolean)"><!-- --></A><H3>
SymmLQ</H3>
<PRE>
public <B>SymmLQ</B>(<A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</A>&nbsp;manager,
              double&nbsp;delta,
              boolean&nbsp;check)</PRE>
<DL>
<DD>Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a> and custom iteration manager. Note that setting
 <code>check</code> to <code>true</code> entails an extra matrix-vector product in
 the initial phase.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>manager</CODE> - the custom iteration manager<DD><CODE>delta</CODE> - the &delta; parameter for the default stopping criterion<DD><CODE>check</CODE> - <code>true</code> if self-adjointedness of both matrix and
 preconditioner should be checked</DL>
</DL>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="getCheck()"><!-- --></A><H3>
getCheck</H3>
<PRE>
public final boolean <B>getCheck</B>()</PRE>
<DL>
<DD>Returns <code>true</code> if symmetry of the matrix, and symmetry as well as
 positive definiteness of the preconditioner should be checked.
<P>
<DD><DL>

<DT><B>Returns:</B><DD><code>true</code> if the tests are to be performed</DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>m</CODE> - the preconditioner, M (can be <code>null</code>)<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a new vector containing the solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A></CODE> - if <code>m</code> is not
 positive definite
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> or <code>m</code> is not
 square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>m</code> or <code>b</code> have
 dimensions inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                        boolean&nbsp;goodb,
                        double&nbsp;shift)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system (A - shift
 &middot; I) &middot; x = b.
 <p>
 If the solution x is expected to contain a large multiple of <code>b</code>
 (as in Rayleigh-quotient iteration), then better precision may be
 achieved with <code>goodb</code> set to <code>true</code>; this however requires an
 extra call to the preconditioner.
 </p>
 <p>
 <code>shift</code> should be zero if the system A &middot; x = b is to be
 solved. Otherwise, it could be an approximation to an eigenvalue of A,
 such as the Rayleigh quotient b<sup>T</sup> &middot; A &middot; b /
 (b<sup>T</sup> &middot; b) corresponding to the vector b. If b is
 sufficiently like an eigenvector corresponding to an eigenvalue near
 shift, then the computed x may have very large components. When
 normalized, x may be closer to an eigenvector than b.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>m</CODE> - the preconditioner, M (can be <code>null</code>)<DD><CODE>b</CODE> - the right-hand side vector<DD><CODE>goodb</CODE> - usually <code>false</code>, except if <code>x</code> is expected to
 contain a large multiple of <code>b</code><DD><CODE>shift</CODE> - the amount to be subtracted to all diagonal elements of A
<DT><B>Returns:</B><DD>a reference to <code>x</code> (shallow copy)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> or <code>m</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>m</code> or <code>b</code> have dimensions
 inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A></CODE> - if <code>m</code> is not
 positive definite
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned</DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solve</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - not meaningful in this implementation; should not be considered
 as an initial guess (<a href="#initguess">more</a>)<DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>m</CODE> - the preconditioner, M (can be <code>null</code>)<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a new vector containing the solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A></CODE> - if <code>m</code> is not positive
 definite
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> or <code>m</code> is not
 square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>m</code>, <code>b</code> or
 <code>x0</code> have dimensions inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector)">solve</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a new vector containing the solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>b</code> has dimensions
 inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, boolean, double)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                        boolean&nbsp;goodb,
                        double&nbsp;shift)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns the solution to the system (A - shift &middot; I) &middot; x = b.
 <p>
 If the solution x is expected to contain a large multiple of <code>b</code>
 (as in Rayleigh-quotient iteration), then better precision may be
 achieved with <code>goodb</code> set to <code>true</code>.
 </p>
 <p>
 <code>shift</code> should be zero if the system A &middot; x = b is to be
 solved. Otherwise, it could be an approximation to an eigenvalue of A,
 such as the Rayleigh quotient b<sup>T</sup> &middot; A &middot; b /
 (b<sup>T</sup> &middot; b) corresponding to the vector b. If b is
 sufficiently like an eigenvector corresponding to an eigenvalue near
 shift, then the computed x may have very large components. When
 normalized, x may be closer to an eigenvector than b.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>b</CODE> - the right-hand side vector<DD><CODE>goodb</CODE> - usually <code>false</code>, except if <code>x</code> is expected to
 contain a large multiple of <code>b</code><DD><CODE>shift</CODE> - the amount to be subtracted to all diagonal elements of A
<DT><B>Returns:</B><DD>a reference to <code>x</code>
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>b</code> has dimensions
 inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned</DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solve</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                        <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)
                 throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                        <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b.
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solve</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - not meaningful in this implementation; should not be considered
 as an initial guess (<a href="#initguess">more</a>)<DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a new vector containing the solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>b</code> or <code>x0</code> have
 dimensions inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solveInPlace</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solveInPlace</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)
                        throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b. The solution is computed in-place (initial guess is modified).
<P>
<DD><DL>
<DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solveInPlace</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the vector to be updated with the solution; <code>x</code> should
 not be considered as an initial guess (<a href="#initguess">more</a>)<DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>m</CODE> - the preconditioner, M (can be <code>null</code>)<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a reference to <code>x0</code> (shallow copy) updated with the
 solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A></CODE> - if <code>m</code> is not
 positive definite
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> or <code>m</code> is not
 square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>m</code>, <code>b</code> or
 <code>x0</code> have dimensions inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector, boolean, double)"><!-- --></A><H3>
solveInPlace</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solveInPlace</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;m,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x,
                               boolean&nbsp;goodb,
                               double&nbsp;shift)
                        throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system (A - shift
 &middot; I) &middot; x = b. The solution is computed in-place.
 <p>
 If the solution x is expected to contain a large multiple of <code>b</code>
 (as in Rayleigh-quotient iteration), then better precision may be
 achieved with <code>goodb</code> set to <code>true</code>; this however requires an
 extra call to the preconditioner.
 </p>
 <p>
 <code>shift</code> should be zero if the system A &middot; x = b is to be
 solved. Otherwise, it could be an approximation to an eigenvalue of A,
 such as the Rayleigh quotient b<sup>T</sup> &middot; A &middot; b /
 (b<sup>T</sup> &middot; b) corresponding to the vector b. If b is
 sufficiently like an eigenvector corresponding to an eigenvalue near
 shift, then the computed x may have very large components. When
 normalized, x may be closer to an eigenvector than b.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>m</CODE> - the preconditioner, M (can be <code>null</code>)<DD><CODE>b</CODE> - the right-hand side vector<DD><CODE>x</CODE> - the vector to be updated with the solution; <code>x</code> should
 not be considered as an initial guess (<a href="#initguess">more</a>)<DD><CODE>goodb</CODE> - usually <code>false</code>, except if <code>x</code> is expected to
 contain a large multiple of <code>b</code><DD><CODE>shift</CODE> - the amount to be subtracted to all diagonal elements of A
<DT><B>Returns:</B><DD>a reference to <code>x</code> (shallow copy).
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> or <code>m</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>m</code>, <code>b</code> or <code>x</code>
 have dimensions inconsistent with <code>a</code>.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> or <code>m</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</A></CODE> - if <code>m</code> is not positive
 definite
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned</DL>
</DD>
</DL>
<HR>

<A NAME="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)"><!-- --></A><H3>
solveInPlace</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A> <B>solveInPlace</B>(<A HREF="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</A>&nbsp;a,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;b,
                               <A HREF="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</A>&nbsp;x)
                        throws <A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A>,
                               <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Returns an estimate of the solution to the linear system A &middot; x =
 b. The solution is computed in-place (initial guess is modified).
<P>
<DD><DL>
<DT><B>Overrides:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">solveInPlace</A></CODE> in class <CODE><A HREF="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</A></CODE></DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the vector to be updated with the solution; <code>x</code> should
 not be considered as an initial guess (<a href="#initguess">more</a>)<DD><CODE>a</CODE> - the linear operator A of the system<DD><CODE>b</CODE> - the right-hand side vector
<DT><B>Returns:</B><DD>a reference to <code>x0</code> (shallow copy) updated with the
 solution
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSelfAdjointOperatorException.html" title="class in org.apache.commons.math3.linear">NonSelfAdjointOperatorException</A></CODE> - if <A HREF="../../../../../org/apache/commons/math3/linear/SymmLQ.html#getCheck()"><CODE>getCheck()</CODE></A> is
 <code>true</code>, and <code>a</code> is not self-adjoint
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/IllConditionedOperatorException.html" title="class in org.apache.commons.math3.linear">IllConditionedOperatorException</A></CODE> - if <code>a</code> is ill-conditioned
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</A></CODE> - if one of the parameters is <code>null</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</A></CODE> - if <code>a</code> is not square
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if <code>b</code> or <code>x0</code> have
 dimensions inconsistent with <code>a</code>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - at exhaustion of the iteration count,
 unless a custom
 <A HREF="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><CODE>callback</CODE></A>
 has been set at construction of the <A HREF="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><CODE>IterationManager</CODE></A></DL>
</DD>
</DL>
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